Ohm's law for ion conduction in lithium and beyond-lithium battery electrolytes.

The viability of next generation lithium and beyond-lithium battery technologies hinges on the development of electrolytes with improved performance. Comparing electrolytes is not straightforward as multiple electrochemical parameters affect the performance of an electrolyte. Additional complications arise due to the formation of concentration gradients in response to dc potentials. We propose a modified version of Ohm's law to analyze current through binary electrolytes driven by a small dc potential. We show that the proportionality constant in Ohm's law is given by the product of the ionic conductivity, κ, and the ratio of currents in the presence (iss) and absence (iΩ) of concentration gradients, ρ+. The importance of ρ+ was recognized by Evans et al. [Polymer 28, 2324 (1987)]. The product κρ+ is used to rank order a collection of electrolytes. Ideally, both κ and ρ+ should be maximized, but we observe a trade-off between these two parameters, resulting in an upper bound. This trade-off is analogous to the famous Robeson upper bound for permeability and selectivity in gas separation membranes. Designing polymer electrolytes that overcome this trade-off is an ambitious but worthwhile goal.

Difference between approximate and rigorously measured transference numbers in fluorinated electrolytes.

The performance of binary electrolytes is governed by three transport properties: conductivity, salt diffusion coefficient, and transference number. Rigorous methods for measuring conductivity and the salt diffusion coefficient are well established and used routinely in the literature. The commonly used methods for measuring transference number are the steady-state current method, t+,id, and pulsed field gradient NMR, t+,NMR. These methods yield the transference number only if the electrolyte is ideal, i.e., the salt dissociates completely into non-interacting anions and cations. In this work, we present a complete set of ion transport properties for mixtures of a functionalized perfluoroether, dimethyl carbonate terminated perfluorinated tetraethylene ether, and lithium bis(fluorosulfonyl)imide (LiFSI). The equations used to determine these properties from experimental data are based on Newman's concentrated solution theory. The concentrated-solution-theory-based transference number, t, is negative across all salt concentrations, and it increases with increasing salt concentration. In contrast, the ideal transference number, t+,id, is positive across all salt concentrations and it decreases with salt concentration. The NMR-based transference number, t+,NMR, is approximately 0.5, independent of salt concentration. The disparity between the three transference numbers, which indicates the dominance of ion clustering, is resolved by the use of Newman's concentrated solution theory.